Re: [理工] [工數]-laplace
1.
let L(x(t))=X
2 5
SX-1 + 3X + --- X= ---
S S
S^2+3S+2 5
---------X = ---- +1
S S
5 S
X=----------- + ----------
(s+1)(s+2) (S+1)(S+2)
1 -1 -1 2
X=5{-----+ ------}+{ -----+ -----}
(s+1) (s+2) (S+1) (S+2)
x(t)=L^-1(X)
=5(e^-t - e^-2t)u(t) -e^-t + 2e^-2t
2. S
SY-1 + Y------- = e^-3s
S^2 + 4
S^3+4S+S
(----------)Y=e^-3s + 1
S^2+4
s^2 + 4 S^2+4
Y=----------e^-3s + --------
S(S^2 + 5) S(S^2+5)
4/5 (1/5)S 4/5 (1/5)S
={------- + ---------- ) e^-3s +{ ---- + ----------}
S S^2 + 5 S S^2 + 5
4 1 4 1
y={--- + --- cos{5^1/2 (t-3) }u(t-3)+ {--- + --- cos(5^1/2 t )
5 5 5 5
有錯請不吝指教
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